The study area was the remote sensing experimental field (34° 13'N, 117° 08'E) near the north gate of Nanhu Campus of the China University of Mining and Technology, Xuzhou city, Jiangsu province, China. The soil type of the study area is cinnamon soil. The climate of Xuzhou is a warm temperate continental monsoon climate, with four distinct seasons and abundant sunshine. The average annual temperature is 14 ℃, and the average annual rainfall is 800~930 mm. The precipitation in the rainy season accounts for 56% of the whole year.

Four areas of 12.0× 11.8 m², 11.8× 11.8 m², 11.8× 11.6 m², and 11.6× 11.6 m² were trimmed of vegetation in the experimental field, and 10 soil samples were selected evenly from each area by the “ plum blossom” sampling method. The four areas included three areas where Cr, Pb, and Zn had been artificially added, respectively, and one normal control area. Plexiglass columns with a diameter of 20 cm and a depth of 20 cm (bottom sealed) were inserted vertically into the soil using a shovel. In October 2013, 30.8 g of chromium(Ⅲ ) chloride hexahydrate, 8.3 g of lead acetate trihydrate, and 16.5 g of zinc sulfate heptahydrate were added to the plexiglass column bottom of the first, second, and third areas, respectively. After this date, no further heavy metals were artificially added. In October 2013 and October 2015, 13— 15 winter wheat seeds of the same type were sown in each plexiglass column. In July 2014 and July 2016, after the wheat had matured, about 1 kg of surface soil was collected from each sampling point. The soil samples were then sealed, marked, and brought back to the laboratory.

Each soil sample was divided into two parts. One part was used to measure the soil reflectance spectra, and the other part was utilized to measure the soil heavy metal concentrations. Before measuring the soil spectra, the samples needed to be dried and ground to pass through a 100-mesh aperture nylon sieve. The soil samples were scanned in the darkroom using a FieldSpec3 Hi-Res Analytical Spectral Devices (ASD) field spectrometer. The instrument covers the 350~2 500 nm range, including 2 151 bands. The soil samples were placed in petri dishes with black velvet underneath to avoid interference from other reflectors. After using a spectralon diffuse reflectance panel to calibrate the reflectance, we collected the spectral data with a contact probe. Each soil sample was scanned 10 times. After removing the abnormal spectra, the average spectrum was taken as the final reflectance spectrum of the soil sample. The spectral curves of the two-stage (i.e., July 2014 and July 2016) soil samples had the same characteristics: at 350~700 nm, where the slope of the spectral curve was steep, there was a weak absorption peak at 480 nm. The spectra rose slowly over 700~1 400 nm. There was then a weak water absorption band at 940 nm. The regions around 1 400 and 1 900 nm were also strongly related to water absorption. The curve began to decrease from 2 200 nm, and there was a distinct absorption peak around 2 200 nm. The results showed that the values of the spectra for the 2016 samples were higher than those from 2014.

Fig.1

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	Fig.1 Spectral curves of the two-stage soil samples

The heavy metals (Cr, Cd, Cu, Pb, and Zn) of the soil samples were detected by inductively coupled plasma-mass spectrometry (ICP-MS). A basic statistical analysis of the heavy metal concentrations of the two-stage soil samples is provided in Table 1. The contents of the five heavy metals in 2016 were significantly higher than those in 2014. According to the experimental design, the heavy metal compounds at the bottom of the plexiglass column slowly migrated up through the soil in the plexiglass column. In 2014, the migration of the heavy metals was not significant. However, by 2016, the heavy metals had migrated upwards and transformed in the soil, which resulted in a sharp increase of the heavy metals in the topsoil (the soil samples collected were topsoil).

Table 1

Table 1

Table 1 Statistical results of the soil heavy metal contents in 2014 and 2016 Year Heavy metal Max Max Mean Std. CV. Cr 15.70 5.90 8.57 2.29 0.27 Cd 0.02 0.01 0.02 0 0.16 2014 Cu 4.40 2.50 3.00 0.43 0.14 Pb 3.40 1.60 2.37 0.38 0.16 Zn 12.80 6.30 9.16 1.45 0.16 Cr 125.50 29.88 50.50 17.46 0.35 Cd 0.2 0.07 0.08 0.02 0.29 2016 Cu 17.01 12.45 15.73 0.95 0.06 Pb 44.82 11.96 16.26 6.89 0.42 Zn 54.03 27.96 34.61 4.57 0.13

Table 1 Statistical results of the soil heavy metal contents in 2014 and 2016

In order to effectively highlight the absorption characteristics of the spectral curves, the soil sample spectra for 2014 and 2016 were processed by continuum removal (CR). Fig.2 shows the average spectra for 2014 and 2016 after CR, where it can be seen that there are several obvious absorption bands, namely, 480, 730, 940, 1 130, 1 400, 1 780, 1 900, and 2 200 nm. Among them, 940, 1 130, 1 400, and 1 900 nm are water absorption bands. Based on the previously published papers^{[4, 9]}, the absorption bands with a higher correlation with heavy metal content are 480, 1 780, and 2 200 nm.

Fig.2

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	Fig.2 Average spectra for 2014 and 2016 after continuum removal

In the visible region, the spectral absorption features are mainly due to the electronic transition of metal ions (such as Fe²⁺, Fe³⁺, Mn³⁺, etc.). The spectral absorption feature of iron/manganese oxides is 480 nm. In the near-infrared range, the absorption characteristics of the soil spectrum are mainly the double frequency and harmonic frequency generated by the molecular bending vibration of molecular groups (C— H, Al— OH, Mg— OH, Fe— OH, C O32-, OH^-, and NH⁴⁺, etc.) in organic matter and clay minerals. The absorption features of 1 780 and 2 200 nm are related to organic matter. The absorption feature around 2 200 nm is caused by the double frequency of the molecular hydroxyl (— OH) stretching vibration of the clay minerals (i.e., silicate minerals). Therefore, we deemed that it was reasonable to use the spectral absorption features of 480, 1 780, and 2 200 nm to estimate the soil heavy metals. In this way, the effects of iron/manganese oxides, organic matter, and clay minerals on the soil heavy metals could be fully considered.

Based on CR, a number of spectral absorption parameters have been developed, including absorption depth (Depth), absorption width (Width), absorption area (Area), and asymmetry (Asym). In this study, we used the absorption peak depths of 480 nm (Depth₄₈₀), 1 780 nm (Depth_{1 780}), 2 200 nm (Depth_{2 200}), and the absorption area of 2 200 nm (Area_{2 200}) to estimate the soil heavy metal concentrations.

1.4.1 Calibration set and validation set

According to the heavy metal content, the 80 soil samples were divided into several groups, with three samples in each group. For each group, two soil samples were selected as training samples (calibration set), and the remaining one was used as the prediction sample (validation set). The sample ratio of the calibration set and validation set was thus 2:1.

1.4.2 Model establishment

Three linear regression methods were used to establish the estimation models between the spectral absorption characteristic parameters and the soil heavy metals. The linear regression methods were least squares (LS), ridge regression (RR), and support vector regression (SVR).

LS is an important parameter estimation method in the linear regression models. The solution process of LS is divided into the following steps. In the first place, the function of the residual squared sum is constructed, and then the method of finding the extremum in differential calculus is used to construct the condition in which the sum of the residuals reaches a minimum. We then obtain the partial derivative function for the parameter estimator and make it equal to zero, thus obtaining the linear equations with respect to the parameter estimator. The LS estimator is obtained by solving the linear equations. If the residual of the linear regression model is e_i, the aim of LS is to make ∑ei2the minimum, to determine the estimators^[11].

RR is a biased estimation model for collinear data analysis. It improves the singularity of the coefficient matrix of the normal equations, which LS is unable to dispose of when estimating the regression coefficients. The matrix (X'X) determinant is relatively small when there is multiple collinearity between the independent variables, and thus the derived data lack stability. RR adds a normal data matrix K_i(0< k< 1, I is the identity matrix) in the sample data matrix to improve the stability of the result^[12].

SVR is an excellent machine learning algorithm based on the Vapnik-Chervonenkis (VC) dimension theory of statistical learning and the principle of structural risk minimization. It performs well in dealing with high-dimensional and small-sample data. The common kernel functions are the linear kernel function, polynomial kernel function, and gaussian kernel function. In order to explain the relationship between the parameters and heavy metal contents, SVR with a linear kernel function was utilized in this study.

1.4.3 Model validation

The models were evaluated with the determination coefficient (R²), the root-mean-square error (RMSE), the mean absolute error (MAE), the residual prediction deviation (RPD), and the ratio of prediction performance to interquartile range (RPIQ). The higher the R² value is, the more stable the model is. The lower the RMSE is, the higher the RPD and the RPIQ are, and the better the prediction performance of the model is.

The two-stage data of the five heavy metals (Cr, Cd, Cu, Pb and Zn) were arranged according to their contents. The absorption depths of 480, 1 780, and 2 200 nm were then investigated. Fig.3 shows the contents of the five heavy metals, of which the first 40 samples and the last 40 were from 2014 and 2016, respectively.

Fig.3

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	Fig.3 The contents of the five heavy metals in 2014 and 2016

In Fig.3, it can be seen that the heavy metal contents are close in each year. However, the comparison between the two-stage data shows that the contents of the five heavy metals in 2016 are significantly higher than those in 2014, especially for Cr, Pb, and Zn, which were added artificially.

The variation trends of the three absorption peaks, along with the heavy metal contents, were analyzed. The effect of iron/manganese oxides on the five heavy metals is shown in Fig.4. The Depth₄₈₀ parameter becomes smaller with the increase of the heavy metal content. This regularity is not obvious over a small range, but it is clearly visible when the difference in the heavy metal content is large, especially at the junction of the two stages.

Fig.4

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	Fig.4 Depth480 parameters of the five heavy metals

It can be seen from Fig.5 that the variation trend of Depth_{1 780} is more pronounced than that of Depth₄₈₀. When the heavy metal content significantly increases, its value decreases. For Pb, the variation trend of Depth_{1 780} is not as straightforward as that of the other four heavy metals. According to Goldschmidt geochemical classification of chemical elements, Pb is a siderophile element. Consequently, Pb has a higher correlation with Depth₄₈₀ than with Depth_{1 780}.

Fig.5

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	Fig.5 Depth1 780 parameters of the five heavy metals

Fig.6

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	Fig.6 Depth2 200 parameters of the five heavy metals

Depth_{2 200} shows an opposite variation tendency compared with the two former parameters. With the increase of the heavy metal content, the value of Depth_{2 200} increases. The Depth_{2 200} value of Cd, Cu, and Zn increases significantly at the junction of the two stages, indicating that these three metals have a higher correlation with organic matter and clay minerals.

The correlation coefficients between the four spectral absorption characteristic parameters and Cu/Zn are higher (Table 2). The correlation coefficients of Pb and Depth₄₈₀ are significantly higher than those of the other three parameters, which shows that Pb is more easily adsorbed by iron/manganese oxides.

Table 2

Table 2

Table 2 Correlation coefficients between heavy metals and spectral absorption characteristic parameters Element Depth480 Depth1 780 Depth2 200 Area2 200 Cr -0.70 -0.70 0.70 0.75 Cd -0.72 -0.74 0.68 0.73 Cu -0.82 -0.82 0.78 0.85 Pb -0.77 -0.59 0.54 0.60 Zn -0.80 -0.81 0.75 0.82

Table 2 Correlation coefficients between heavy metals and spectral absorption characteristic parameters

Linear regression models were established between the soil heavy metal concentrations and the two soil spectral absorption characteristic parameters that had the highest correlation with each heavy metal. The regression coefficients were calculated using LS. The models and model evaluation are shown in Table 3. It is found that Depth₄₈₀ has a higher estimation accuracy for Cr and Pb, indicating that the adsorption effect of the iron/manganese oxides for Cr and Pb is greater than that of organic matter and clay minerals. The accuracy of estimating Cd, Cu, and Zn by Area_{2 200} and Depth_{1 780} is higher. These three heavy metals belong to the sulfophilic elements, and Cu in soil mainly exists as an organic-bound state. Therefore, for Cd, Cu, and Zn, the adsorption capacity of organic matter and clay minerals is higher than that of iron/manganese oxides.

Table 3

Table 3

Table 3 Results of the linear regression between soil heavy metal contents and single parameters Element Parameter RC2 RMSEC MAEC RP2 RMSEP MAEP RPD RPIQ Formula Cr Depth480 0.45 18.75 12.84 0.64 13.77 10.81 1.60 2.65 Y=-384.98X+124.51 Area2 200 0.64 15.25 10.52 0.47 18.89 14.80 1.16 1.93 Y=19.27X-61.20 Cd Depth1 780 0.55 0.03 0.02 0.60 0.02 0.02 1.42 2.59 Y=-5.20X+0.13 Area2 200 0.48 0.03 0.02 0.74 0.02 0.02 1.72 3.14 Y=0.03X-0.07 Cu Depth1 780 0.68 3.64 2.78 0.68 3.69 2.82 1.73 3.55 Y=-988.35X+23.20 Area2 200 0.74 3.29 2.63 0.69 3.70 3.03 1.72 3.54 Y=5.24X-15.70 Pb Depth480 0.58 5.95 4.16 0.72 4.00 3.12 1.70 2.90 Y=-157.59X+49.02 Area2 200 0.32 7.52 4.48 0.56 4.81 3.72 1.41 2.41 Y=4.39X-11.47 Zn Depth1 780 0.69 7.41 5.94 0.60 8.19 6.69 1.55 3.12 Y=-1 953.69X+49.73 Area2 200 0.72 7.03 5.62 0.55 8.62 6.80 1.47 2.96 Y=9.64X-24.24

Table 3 Results of the linear regression between soil heavy metal contents and single parameters

In order to enhance the stability of the model and the interpretability of the variables, the four parameters of Depth₄₈₀, Depth_{1 780}, Depth_{2 200}, and Area_{2 200} were applied to estimate the soil heavy metals. The regression coefficients were calculated by LS, RR and SVR. The estimated results are shown in Table 4.

Table 4

Table 4

Table 4 Results of the regression between the soil heavy metal contents and the four parameters Element model RC2 RMSEC MAEC RP2 RMSEP MAEP RPD RPIQ LS 0.70 13.94 8.94 0.71 12.91 9.45 1.70 2.83 Cr RR 0.70 13.94 8.95 0.71 12.92 9.47 1.70 2.83 SVR 0.69 18.34 15.62 0.66 13.19 8.69 1.67 2.77 LS 0.69 0.02 0.01 0.83 0.01 0.01 2.24 4.09 Cd RR 0.68 0.02 0.01 0.84 0.01 0.01 2.26 4.12 SVR 0.65 0.02 0.01 0.84 0.02 0.01 2.16 3.93 LS 0.93 1.75 1.36 0.92 1.85 1.57 3.45 7.09 Cu RR 0.92 1.76 1.38 0.92 1.77 1.47 3.59 7.39 SVR 0.90 2.36 1.80 0.91 1.93 1.61 3.30 6.79 LS 0.62 5.61 3.37 0.80 3.41 2.78 1.99 3.40 Pb RR 0.62 5.61 3.39 0.80 3.39 2.78 2.00 3.41 SVR 0.60 5.82 3.76 0.73 4.16 3.60 1.63 2.78 LS 0.86 4.97 3.93 0.88 4.43 3.84 2.87 5.77 Zn RR 0.86 4.97 3.93 0.89 4.38 3.78 2.90 5.83 SVR 0.82 8.00 6.80 0.88 4.72 3.59 2.69 5.42

Table 4 Results of the regression between the soil heavy metal contents and the four parameters

The accuracy of the models using the four spectral absorption characteristic parameters are much better than the results of the models using only a single parameter. The results show that stable heavy metal estimation models can be established by considering the influence of the iron/manganese oxides, organic matter, and clay minerals on soil heavy metal content. Except for Cr, the RP2values of the estimation models for the other four heavy metals are all above 0.8, and the RPD of these models all reach 1.5 or more, which confirms that the prediction performance of these models is good. The prediction performance for Cu is superior to that for the other metals, with RP2reaching 0.92. Among the three models, RR is the best and most stable model.